Exercise 38 introduced two machines that produce wine corks, the first one having a normal diameter distribution

Question:

Exercise 38 introduced two machines that produce wine corks, the first one having a normal diameter distribution with mean value 3 cm and standard deviation .1 cm, and the second having a normal diameter distribution with mean value 3.04 cm and standard deviation .02 cm. Acceptable corks have diameters between 2.9 and 3.1 cm. If 60% of all corks used come from the first machine and a randomly selected cork is found to be acceptable, what is the probability that it was produced by the first machine?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...